Understanding behavior of vehicle traffic flow has been of significant interest to scientists, transportation researchers, transportation engineers, road engineers, urban planners, policy makers, computer scientists, economists, vehicle manufacturers, and commuters who rely on transportation on a daily basis. As used herein, “vehicle traffic flow” refers to movement of vehicles between two points or traffic intersections. Also, as used herein, “traffic intersection” refers to a junction between two or more roads that meet or cross each other. Traffic jam and traffic phase transitions affect people who encounter traffic jams daily on city, urban and highway roads. With the advent of wirelessly connected and autonomous vehicles with vehicle-to-vehicle (V2V) communications and advanced driver assistance systems (ADAS), both behavior and modeling of vehicle traffic flows are deemed to change dramatically. Vehicle traffic flow is typically controlled by traffic signals at traffic intersections using a computer controlled preprogrammed timer sequence. The traffic signals defined, for example, by a green traffic signal light, a yellow traffic signal light, and a red traffic signal light are timed to change their sequence after a predetermined time period to regulate the vehicle traffic flow, for example, by retaining a long duration of the green traffic signal light for long roads with heavy vehicle traffic flow and a short duration of the green traffic signal light for short roads with low vehicle traffic flow. The predetermined time period is set after an extensive examination of vehicle traffic flow patterns at respective traffic intersections. The timing of the traffic signals is varied with the computer controlled preprogrammed timer sequence to regulate vehicle traffic flow during peak hours and scheduled events at the respective traffic intersections. Actions and efforts to improve traffic throughput, that is, an integral of traffic flow flux, via the traffic signals are predetermined and preprogrammed. Conventional traffic signal control systems use inductive loop detectors or video cameras to detect vehicles in a particular direction. When there are no vehicles in any of the directions, the traffic signal lights need to be dynamically changed to red to allow vehicles waiting for green traffic signal lights on other cross directions to pass through. The conventional traffic signal control approach may improve the traffic throughput provided traffic is low, that is, for a vehicle traffic flow with a near-zero flow density, and provided the traffic is asymmetric, that is, when the vehicles wait for red traffic signal lights in a particular direction and there are no vehicles in the cross directions. The conventional traffic signal control approach does not apply to most of the traffic cases where the traffic is congested and needs an optimized vehicle traffic flow control. A congested vehicle traffic flow with a moderate traffic flow density is well defined as the traffic flow speed cannot reach the predefined speed limit for that road.
Traffic signals are typically time dependent and do not cater to real world traffic conditions. For example, the traffic signals typically do not consider traffic influencing factors, for example, human factors, road conditions, vehicle traffic flow at other proximal traffic intersections, etc. Furthermore, the traffic signals typically depend on historic data examined and preprogrammed with a predetermined time at the respective traffic intersections and do not cater to a real time vehicle traffic flow pattern that results from a growing number of vehicles including human driven vehicles and autonomous vehicles on the roads. Individually, drivers of the vehicles spend a significant amount of time at traffic signals waiting for a traffic signal light to turn green, even though there is no actual vehicle traffic flow at traffic intersections in other directions. Furthermore, conventional vehicle traffic flow control methods lack efficient utilization of an unutilized pass-through efficiency for an oncoming direction with an asymmetric left-turn, where a left-turn signal is longer for a heavy traffic direction, and for cross directions by shortening a green traffic signal light duration as long as the shortened duration does not cause accumulation of vehicles for other directions. The un-optimized traffic signal light control results in frustrated drivers and possible further traffic jam, rash driving, and eventual accidents. Collectively, the overall traffic throughputs in all directions of a traffic intersection and proximal traffic intersections are far from optimized while considering symmetric and asymmetric vehicle traffic flows in opposite directions and as well as their upstream and downstream traffic intersections.
Moreover, a longer wait time of the vehicles translates to wasted gasoline and an increase in air pollution. Traffic signals at traffic intersections are configured based on a fundamental diagram of vehicle traffic flow, which is typically used as a standard for designing traffic models in the transport and research industry. The fundamental diagram of vehicle traffic flow is a diagram that provides a relation between the traffic flow flux, that is, vehicles per hour or vehicles per second, and a traffic flow density, that is, vehicles per kilometer (km) or length percentage of vehicles occupying a road lane. Vehicle traffic flows were first studied in 1935 by Greenshield, who based his study on a phenomenological model which assumed a linear traffic flow density-traffic flow speed relation with one fitting parameter, resulting in a quadratic relation between the traffic flow flux and the traffic flow density, since the traffic flow flux is a product of the traffic flow density and the traffic flow speed. The traffic flow flux-traffic flow density curve resulting from an assumed or curve-fitting traffic flow density-traffic flow speed relation is referred to as the fundamental diagram in transportation research and control. Greenshield's model was refined by many others using various traffic flow density-traffic flow speed relations with more modeling parameters. Van Aerde's model significantly improved Greenshield's model from a symmetric fundamental diagram shape to an asymmetric fundamental diagram shape by assuming a non-linear traffic flow density-traffic flow speed with four fitting parameters. In conventional fundamental diagram models, for a given traffic flow density, there is one and only one corresponding traffic flow speed and traffic flow flux, or vice versa.
Starting in the 1950s, fluid-dynamical models with numerical methods were employed to study a phase transition from a laminar flow, that is, a well-ordered state, to start-stop motions, that is, a disordered state, and the resultant density waves with increasing traffic flow density. In these approaches, a density-speed relation is either assumed or numerically fitted. More recently, computer simulations have been applied to the study of vehicle traffic flows. Nagel and Schreckenberg proposed the cellular automaton model using stochastic discrete simulation. The cellular automaton model qualitatively reproduces some macroscopic properties of vehicle traffic flows such as a transition from a smooth motion to start-stop motions. The density wave method was also employed to numerically calculate a shock wave decay in a metastable region in a car-following model. However, none of the existing models has been able to obtain a theoretical relation for the traffic flow flux-traffic flow density relation, or for a minimum safe driving distance between consecutive vehicles in a vehicle traffic flow. Many other models have realized the importance of human reaction time in vehicle traffic flow behavior, but are still unable to obtain its effect on road capacity.
As disclosed above, the fundamental diagram of vehicle traffic flow was previously empirically derived based on computer simulations, traffic modeling, etc., and does not take into account multiple traffic influencing factors, for example, dry or wet road conditions, drivers' reaction times, etc., which have significant effects on the vehicle traffic flow. In the fundamental diagram of vehicle traffic flow, a traffic flow speed corresponds to one and only one traffic flow density and vice versa. It is incorrect to assume one traffic flow flux corresponds to one traffic flow density or one traffic flow speed, as traffic flow flux may correspond to many traffic flow densities or traffic flow speeds with an upper bound based on experimental observations and computer simulations. Therefore, there is a need for analytically deriving upper boundary flux-density curves instead of modeling and curve-fitting averaged flux-density curves so that phase transitions and traffic jams for vehicles traffic flows can be both qualitatively and quantitatively investigated. Conventional methods used for representing different traffic flow phases and establishing a relation between traffic flow flux and traffic flow density, rely on an empirically derived representation, for example, a triangle peak, etc., with no valid scientific reasoning. These conventional methods do not represent a transition in traffic flow phases without introducing additional modeling parameters and an assumption that road capacity equals the traffic flow flux at the triangle's peak. Furthermore, these conventional methods are not supported with quantitative analysis data to predict transitions across traffic flow phases efficiently.
Conventional methods for analyzing traffic jams have relied upon empirically-derived models and computer simulations. Traffic jams are not only due to crowding of vehicles on the road, but also due to the manifestation of an upper boundary in a traffic flow flux-traffic flow speed plane, from which quantitative conditions and properties, such as critical densities, jam speeds, jam densities, and density waves, for the occurrence of a traffic jam can be rigorously derived. When a traffic jam occurs, the traffic flow speed cannot reach the designated speed limit due to a high traffic flow density, but not necessarily due to a high traffic flow flux, since the traffic flow flux q=ρv, where ρ is the traffic flow density and v is the flow speed. Severely congested traffic may result in a traffic jam, that is, “stop-and-go” traffic behavior. Congested vehicle traffic flows have been investigated both experimentally and via modeling, wave theory, fluid dynamics, and computer simulations. In particular, three traffic flow phases, for example, “free flow,” “synchronized flow”, and “jam flow” have been experimentally identified and statistically investigated by means of computer simulation. These simulations have qualitatively reproduced experimental observations of the phase transitions by adjusting various model parameters, for example, up to 10 model parameters. However, these simulations could not provide definitive conditions or analytical solutions on these phase transitions, because many model parameters had to be introduced. Furthermore, their use of a triangle with the base of the triangle as the axis of the traffic flow density or an empirically-derived curve to represent the relationship between the traffic flow flux and the traffic flow density defined as the fundamental diagram is born out of a need for convenient representation, without a valid scientific basis. Moreover, road capacity is assumed to be the traffic flow flux at the triangle's peak, where the traffic flow speed is at the traffic free flow speed, which is an inaccurate assumption. There is a need for using the traffic flow density or the traffic flow speed as a variable to maximize the traffic flow flux for vehicle traffic flows.
Predicting vehicle traffic flow at traffic intersections and controlling traffic signals using different factors locally and globally via wireless connections that influence the vehicle traffic flow significantly reduces the amount of vehicle emissions, minimizes the traffic jam, enhances the safety of commuters, and reduces travelling time and waiting time at traffic intersections. To maintain a smooth moving and optimized traffic flow flux at traffic intersections, there is a need for dynamically configuring traffic signals using multiple traffic influencing factors and for an enhanced method that predicts the transitions of vehicle traffic flow across traffic flow phases comprising, for example, a traffic free flow phase, a synchronized traffic flow phase, a jam traffic flow phase, etc., based on quantitatively analyzed traffic influencing factors, and accordingly varies the timing of the traffic signals at their respective traffic intersections.
Hence, there is a long felt but unresolved need for a method and a traffic prediction and control system for predicting and controlling vehicle traffic flow through a traffic intersection dynamically with proximal traffic intersections. Moreover, there is a need for optimizing control of traffic signal lights in real time by utilizing a concerted network method rather than an individually preprogrammed method. Furthermore, there is a need for a centralized traffic monitoring system that takes over functioning of a traffic signal at a traffic intersection that malfunctions due to malfunctioning of computer controlled timers programmed with a predetermined timing sequence. Furthermore, there is a need for generating an analytical fundamental diagram and a traffic phase diagram that predict a traffic flow flux and transitions of traffic flow phases in real time considering both human driven vehicles and wireless autonomous vehicles.